Investors have traditionally measured the performance of bond portfolios, as well as those who manage them, on the basis of the total return they generate over time, where the term “total” is used to refer to the overall return from an investment regardless of its source. For example, the annual total return on a bond may include both the coupons paid during the applicable year and the value change during the applicable year. In which case, as shown in Equation 1 below, the total return would equal the coupon return plus the value change divided by the bond's value at the beginning of the year.Total Return=(coupon return+value change)/beginning value  (1)
To further illustrate the concept of total return, an example total return calculation using Equation 1 is provided below. In the example, a $100 par bond with a 5% coupon that is to be paid annually at the end of the year has a market value equal to its face value of $100 at the beginning of the year. The market value of the bond increases to $102 by year's end and the 5% coupon is paid. Accordingly, the coupon return equals five dollars, the value change equals two dollars, and the total return equals seven percent.
$100 par bond, 5% coupon paid annually at year end
$100 invested at beginning of year
$100 bond market value at beginning of year
$102 bond market value at end of yearTotal Return=(($100*.05)+($102−$100))/$100=(5+2)/100=0.07=7.00%
In the foregoing example the total return is shown to have two components: a coupon return component and a price return component. Total return is of interest to investors as it represents the change in their overall economic position resulting from an investment. However, the individual components that comprise total return are also of interest to many investors. The coupon return equates to investor cash flow and is the main component of current accounting income. However, value change (price return) does not equate to cash flow and does not represent accounting income, since the price return is not realized unless the bond is sold.
Many bond investors, such as insurance companies, are yield-focused investors who want to maximize their ongoing investment income. Accordingly, they are primarily concerned with the coupon component of total return rather than the price return component. Additionally, stakeholders in the bond investor's company such as analysts and shareholders generally place greater value on investment income than on realized gains or losses, since the former represents recurring income, whereas the latter represents what is often considered a non-recurring item. Hence, information pertaining to the coupon component of return is of primary interest to many investors, since it is related to the recurring realized investment income associated with the bond portfolio.
However, the recurring realized investment income of a bond is not determined solely by the coupon component of return, but is also dependent upon the amortization, if any, associated with the bond. When a bond is purchased at other than its face (par) value, the beginning book value (generally, its purchase price) of a bond is systematically amortized towards its par value over the life of the bond so that on its maturity date the bond's book value is equal to par value. If the bond was purchased at a premium, the recurring realized investment income is reduced by the amount of the amortization and if the bond was purchased at a discount, the recurring realized investment income is increased by the amount of the amortization. (Amortization that increases the book value of an investment is often referred to as “accretion”).
The “book yield” is a measure of a bond's recurring realized investment income that combines both the bond's coupon return plus its amortization. It is defined as the bond's Internal Rate of Return (IRR) of all its cash flows. The following example illustrates the concept of book yield. A $100 par bond having a 5% coupon to be paid annually at year end is purchased for a $95 purchase price at the beginning of the year. The bond is set to mature in three years. In this example, the book yield will be greater than the 5% coupon on the discount bond as the investor will receive both the 5% coupon and the difference between purchase price and maturity value (an additional $5). The book yield at purchase will be 6.90%, which is the internal rate of return or IRR of the cash flows. The $5 discount is amortized into income over the life of the bond and the book value of the bond is increased until it reaches its par value of $100 at maturity.
Accounting systems calculate a bond's book yield when a bond is first purchased. The calculated book yield for an individual investment is then multiplied by the book value of that investment to derive the accounting income to be recorded from that investment. This calculation is typically depicted in an amortization table showing the amount of income and changes to the book value over time for amortization. An amortization table for the above example is provided below in Table 1.
TABLE 1Assumptions5% annual coupon bond, $100 par value, maturity of 3 years, purchased for $95Book ValueIncomeBegEndBookCashPeriodBookAmortBookCouponAmortIncomeYieldFlow0(95.00)195.001.5696.565.001.566.566.90%5.00296.561.6698.225.001.666.666.90%5.00398.221.78100.005.001.786.786.90%105.006.90%IRR
Even though a bond's book yield through maturity is calculated when the bond is first purchased, the book yield is not necessarily static and it may have to be recalculated. Indeed, for bonds that allow prepayment of principle, such as mortgage backed securities (MBS), the IRR and the book yield typically do vary over the life of the investment. A simple MBS, or pass-through MBS is a bond backed by a pool of residential mortgage loans. The underlying loans will have a stated or nominal maturity. For example, the nominal maturity is 30 years for a pool of 30 year mortgages. However, on average the pool will be paid down much sooner than 30 years as many mortgagors prepay their loans through refinancing, selling their house, and making extra principal payments. Estimating how quickly the pool will be paid down, or the pool's prepayment speed, is desirable when investing in these securities. For MBS bond investments at other than par (premium or discount), the book yield on these securities will change as prepayment speeds change. An illustrative example follows.
Assume that an MBS bond is purchased for $105 with a par of $100. At the time of purchase the average life of the underlying pool of mortgages is 10 years. The accounting that ensues at purchase date is to amortize the $5 premium over the 10 year average life of the investment utilizing the bond's IRR. Assume that that same MBS bond is held by the investor one year later and that prepayment speeds have increased (i.e. interest rates have fallen and many mortgagors are refinancing) such that the average life of the underlying pool of mortgages has dropped to five years from ten years. The accounting is now revised with the amortization of the premium now occurring over a period that is ½ what was originally anticipated. The revised faster amortization changes the book yield of the bond. The direction of book yield change is a function of whether the bond was purchased at a premium or discount and whether prepayment speeds increased or decreased as illustrated Table 2 below.
TABLE 2Prepayment SpeedsPrepaymentIncreaseSpeeds DecreasePurchased atBook Yield DecreasesBook Yield IncreasesPremium over parPurchased atBook Yield IncreasesBook Yield DecreasesDiscount from par
Not only can the book yield for a bond portfolio change due to changes in the book yields of the individual bonds that comprise the portfolio, the book yield for a bond portfolio can change even if the book yields of the individual bonds that comprise the portfolio remain constant. This is true because the book yield of a portfolio is the weighted average of the book yields of the bonds that comprise the portfolio, where the weighting factor for an individual bond is the book value of the individual bond divided by the book value of the bond portfolio (the book value of the bond portfolio is equal to the sum of the book values of the individual bonds). Since the book value of a bond that was not purchased at face value varies over time based on its amortization, the weighting factor for that bond as well as the weighting values for all of the other bonds in the portfolio will change over time. Accordingly, the book yield for a portfolio that contains bonds not purchased at face value will change over time even if the book values of all the individual bonds do not change.
There is a long felt yet unmet need for systems and methods that provide information as to how book yield of a portfolio changes over time and why those changes occur.